Thesis advisor: Ian Biringer / In this thesis we study the class of 3-manifolds that admit a compact exhaustion by hyperbolizable 3-manifolds with incompressible boundary and such that the genus of the boundary components of the elements in the exhaustion is uniformly bounded. For this class we give necessary and sufficient topological conditions that guarantee the existence of a complete hyperbolic metric. / Thesis (PhD) — Boston College, 2019. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 103-106). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 164-165).

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Low, Ho Chi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 76-79). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

Yiu, Fa Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 55-58). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Elementary properties and notations of Hyperbolic space --- p.9 / Chapter 3 --- Poisson kernel and Conformal densities --- p.16 / Chapter 3.1 --- Poisson kernel --- p.17 / Chapter 3.2 --- Conformal densities --- p.19 / Chapter 4 --- Patterson construction and decomposition --- p.27 / Chapter 4.1 --- Patterson construction --- p.27 / Chapter 4.2 --- Patterson decomposition --- p.33 / Chapter 5 --- Bonahon surfaces and Grided surfaces --- p.39 / Chapter 5.1 --- Bonahon surfaces --- p.40 / Chapter 5.2 --- Grided surfaces --- p.46 / Chapter 6 --- Margulis number of Hyperbolic Manifolds --- p.51 / Margulis Number for Hypcrbolic 3-manifolds --- p.5 / Chapter 6.1 --- Gcomertrically finite groups --- p.51 / Chapter 6.2 --- Margulis number of Closed Hyperbolic Manifolds --- p.53 / Bibliography --- p.55

Suen, Chun Kit Anthony. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 89-92). / Abstracts in English and Chinese. / Abstract --- p.iii / Abstract --- p.iv / Acknowledgements --- p.v / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Morse Homology --- p.5 / Chapter 2.1 --- Introduction --- p.5 / Chapter 2.2 --- Classical Morse Theory and Morse Functions --- p.5 / Chapter 2.3 --- Handlebody Decomposition for 3-manifold --- p.7 / Chapter 2.4 --- Stable manifold and Unstable manifold --- p.10 / Chapter 2.5 --- Trajectory flows and the Morse-Smale-Witten Complex --- p.11 / Chapter 3 --- Lagrangian Floer Homology --- p.22 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Preliminaries on Symplectic Geometry --- p.23 / Chapter 3.2.1 --- Basic Definitions --- p.23 / Chapter 3.2.2 --- The Symplectic Group --- p.26 / Chapter 3.2.3 --- Maslov index for non-degenerate paths in Sp(2n) --- p.28 / Chapter 3.2.4 --- Maslov index - the analytic aspect --- p.35 / Chapter 3.3 --- Definition of Floer Homology --- p.37 / Chapter 3.4 --- Some Remarks --- p.41 / Chapter 4 --- Heegaard Floer Homology --- p.43 / Chapter 4.1 --- Introduction --- p.43 / Chapter 4.2 --- Basic Set-Up --- p.43 / Chapter 4.3 --- Topological Preliminaries --- p.44 / Chapter 4.3.1 --- Symmetric Product --- p.44 / Chapter 4.3.2 --- The Tori Tα and Tβ --- p.47 / Chapter 4.3.3 --- Intersection Points and Disks --- p.48 / Chapter 4.3.4 --- Domains --- p.52 / Chapter 4.3.5 --- Spinc Structures --- p.54 / Chapter 4.3.6 --- Holomorphic Disks and Maslov Index --- p.63 / Chapter 4.4 --- Definition of Heegaard Floer Homology --- p.65 / Chapter 4.4.1 --- The chain complex CF --- p.66 / Chapter 4.4.2 --- The chain complex CF∞ --- p.67 / Chapter 4.4.3 --- The chain complexes CF+ and CF- --- p.68 / Chapter 4.4.4 --- Some Remarks --- p.70 / Chapter 5 --- Examples and Applications --- p.72 / Chapter 5.1 --- Introduction --- p.72 / Chapter 5.2 --- The homology three-spheres --- p.72 / Chapter 5.2.1 --- The sphere S3 --- p.72 / Chapter 5.2.2 --- The Poincare sphere and the Brieskorn spheres --- p.74 / Chapter 5.2.3 --- Long exact surgery sequence and the absolutely graded Hee- gaard Floer homology --- p.78 / Chapter 5.3 --- More Application --- p.84 / Chapter 5.3.1 --- Knot Floer homology --- p.84 / Chapter 5.3.2 --- Invariants on 4-manifolds --- p.86 / Chapter 5.4 --- Further developments --- p.87 / Bibliography --- p.89